Bound states with complex frequencies near the continuum on lossy periodic structures

TL;DR

This paper investigates how small material losses affect bound states in the continuum (BICs) in periodic structures, revealing different behaviors for symmetry-protected and non-symmetry-protected BICs and enhancing understanding for practical use.

Contribution

It introduces a perturbation method to analyze the impact of material loss on BICs, distinguishing behaviors based on symmetry protection, and provides numerical illustrations.

Findings

Symmetry-protected BICs maintain real Bloch wavevectors with complex frequencies.

Non-symmetry-protected BICs typically develop complex Bloch wavevectors with complex frequencies.

Bound states with complex frequencies appear near the continuum due to material loss.

Abstract

On a lossless periodic dielectric structure sandwiched between two homogeneous media, bound states in the continuum (BICs) with real frequencies and real Bloch wavevectors may exist, and they decay exponentially in the surrounding homogeneous media and do not couple with propagating plane waves with the same frequencies and wavevectors. The BICs are of significant current interest, because they give rise to high-$Q$ resonances when the structure or the Bloch wavevector is slightly perturbed. In this paper, the effect of a small material loss on the BICs is analyzed by a perturbation method and illustrated by numerical results. It is shown that bound states with complex frequencies near the continuum appear, but they behave differently depending on whether the BIC is symmetry-protected or not. The Bloch wavevector of a bound state with a complex frequency can be real if the original BIC is symmetry-protected, and it is usually complex if the original BIC is not symmetry-protected. Our study improves the theoretical understanding on BICs and provides useful insight for their practical applications.